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Stylized facts in ecology

In economics and other social sciences, “stylized facts” are broad empirical generalizations that are essentially true, although they may be inaccurate in some details, gloss over some nuances, or have some exceptions. The term was coined by Kaldor (1961), who identified several stylized facts about macroeconomics; they’re now known as the “Kaldor facts”.

Stylized facts are widely seen as a key raw material for healthy social scientific research (Summers 1991, Abad & Khalifa 2015). Stylized facts give theory a target to shoot at–something to explain. Indeed, the most useful ones will suggest (though of course not prove) theoretical hypotheses that might explain them. Stylized facts allow you to evaluate theory: your theory is importantly wrong if it can’t reproduce all the stylized facts it should reproduce. Stylized facts guide theory improvement: knowing which stylized facts your theory does and doesn’t reproduce suggests ideas for how to improve your theory. Finally, stylized facts aid feedback from theory to empirical work. Theory that predicts new stylized facts for empiricists to look for is highly valued. Theory that’s hard to test because it doesn’t predict any new stylized facts is much harder to test and so much less valued. Summers (1991) basically argues that if empiricists aren’t producing stylized facts, and theorists aren’t explaining and predicting stylized facts, they’re both Doing It Wrong.

I wouldn’t go that far. But I do think Summers and the many economists who think as he does have a point from which ecology could draw some lessons.

Where do our stylized facts come from in ecology? One obvious answer is “meta-analyses”, but I’m not so sure about that. In a recent post I noted that meta-analyses in ecology often don’t produce stylized facts that give new theory a “target to shoot at”, and so often end up functioning more as endpoints rather than as jumping-off points for further theoretical and empirical work. Which I guess is fine if you don’t expect or want ecological research to do more than statistically summarize what happens at various places and times. But personally, and without denying the value of those summaries, I’d think ecologists sometimes can and should do more than that. I don’t agree that the undoubted complexity and variability of our study objects entails that ecology will never be anything more than a bunch of unique case studies that defy any theorizing. (aside: I recognize that there are other purposes meta-analyses can and do sometimes serve, such as testing existing theory and summarizing information bearing on a specific management issue.)

Then again, perhaps we shouldn’t be looking to meta-analyses for stylized facts. Abad & Khalifa (2015) argue that we should distinguish stylized facts from “bare facts”. They say that stylized facts, in contrast to bare facts, are not validly and rigorously inferred from reliable data. Lack of a rigorous basis in reliable data is what makes a stylized fact stylized. They also say that stylized facts aren’t merely facts a theory ought to explain (as with bare facts), but that stylized facts play a “methodologically beneficial role” above and beyond giving theory something to explain. And here’s the clincher: they argue that the stylization of stylized facts is crucial to their methodologically beneficial role. Basically, stylized facts give you something to go on when otherwise you wouldn’t have anything to go on. Having something to go on is really valuable.*

So, what are ecology and evolution’s most important, interesting, or fruitful stylized facts? Some opening bids:

My favorite stylized fact in ecology is from Murdoch et al. (2002): generalist consumers that exhibit cyclic population dynamics cycle with low amplitude and short period. In contrast, specialist consumers that cycle do so with high amplitude and long period. (those could be stated more precisely, but that’s close enough for government work)

My second-favorite stylized fact is closer to being a stylized fact in Abad & Khalifa’s sense: a plausible empirical claim that might be true, and that provides a particularly fruitful basis for theorizing. It’s Bjørnstad’s (2000) observation that large-scale spatial synchrony of cycling populations is lost if those populations stop cycling. The recent collapse of population cycles of many European mammals provides an opportunity to test whether this actually is a fact.

Most of the other stylized facts on my list are less stylized and better-grounded in reliable data than the one from Bjørnstad (2000), and so fall more towards the “bare facts” end of the continuum from bare facts to stylized facts:

Another stylized fact from population ecology: negative density dependence is ubiquitous, although mostly too weak and/or restricted to low population sizes to distinguish against the background of sampling error given the typical length of ecological time series (Hatton et al. 2015, Ziebarth et al. 2010).

Many stylized facts in ecology are from macroecology and biogeography; ecologists usually call them “large-scale patterns”. Many of them are very well-established and so very much towards the “bare facts” end of the spectrum. Species abundance distributions comprise a few common species and many rare ones (or more precisely, they always have something approximating a lognormal or logseries distribution). Species richness increases as a power law function of area with an exponent of about 0.25 (aside: is “quantitative stylized fact” an oxymoron?) Species richness is highest at low latitudes. Bergmann’s Rule. In my anecdotal experience, macroecologists and biogeographers are very proud of their stylized facts and like to think they have more of them than other subfields of ecology. 🙂

Many stylized facts in ecology involve comparing different species. And many of the most fruitful comparative stylized facts (meaning, the ones that have inspired the most successful theory) are those from evolutionary ecology. Though many of those arguably are too quantitative to be considered “stylized”. Quarter-power allometric scaling. Rensch’s Rule. Life history invariants. The island rule.

I used to be a food web ecologist, so I know a bunch of stylized facts about food webs. Food web connectance ranges from about 0.03 to about 0.3. Connectance declines on average with increasing species richness because high-connectance, high-richness food webs don’t exist. Food chains are short (just a few links, usually). All food webs fall into one of two structural classes (roughly, those with lots of omnivory and poorly-defined trophic levels, and those with little omnivory and well-defined trophic levels).

Contrary to what you might think, community ecology has some stylized facts, though perhaps they tend to be more stylized than those from, say, macroecology. Trophic cascades are ubiquitous, but attenuate as they propagate to lower trophic levels (Shurin et al. 2001). Total biomass, productivity, or resource use of a trophic level increases in a saturating fashion with increasing species richness of the trophic level, all else being equal.

Community ecology also provides many examples of what Abad and Khalifa (2015) call “discredited stylized facts”–stylized facts that turned out, upon further empirical investigation, not to be facts at all, so got discarded rather than getting converted into bare facts. Or rather, they should have been discarded, but they haven’t been–they live on as zombie ideas, or perhaps as ghost ideas. The IDH,humped diversity-productivity curves, and predominantly linear local-regional richness relationships are three examples. Those research programs all kicked off because of a few suggestive empirical examples–stylized facts. This illustrates one of the occupational hazards of basing the early stages of a research program on stylized facts: if the facts turn out not to be facts at all, you’re hosed–but the research program is likely to keep on keepin’ on for a long time because research programs have their own internal momentum.

It’s interesting to think in a comparative way about stylized facts. For instance, are there different types? Tentatively, I’d suggest that many stylized facts of macroecology are what Steven Frank would call “statistical attractors” analogous to the central limit theorem (a suggestion that I’m far from the first to make, of course). These stylized facts are explained by “multiple realizability”. Roughly, there are many possible worlds in which these stylized facts are facts, and few or no possible worlds in which they’re not facts. In contrast, I think of the stylized comparative facts of evolutionary ecology as reflecting the strong constraints that evolution by natural selection places on the possibilities. Rather than there being many roads leading to the same endpoint (and no roads leading any other direction), there’s only one road leading to the endpoint; all other roads lead to dead ends. But some stylized facts don’t fall into either class, or at least it’s not obvious to me that they do.

*To say that one shouldn’t leap into theorizing until one has more to go on than stylized facts implies an overly-inductivist, empiricist view of how successful research programs proceed. That overly-inductivist view was expressed by some of Charles Darwin’s opponents following publication of the Origin of Species. They claimed that Darwin was speculating wildly, deviating from the slow but sure path of first accumulating a mass of facts without any preconceived ideas as to what might explain them, how they might relate to one another, or even what facts were worth accumulating in the first place. Darwin in contrast famously referred to evolution by natural selection as “a theory by which to work”–an idea that made sense of the available stylized facts and provided guidance as to the most productive new lines of empirical and theoretical investigation. Thereby allowing the research program to reach an ideal endpoint–well-established “bare facts” plus a well-tested theory to explain them–more quickly than it otherwise would have. History justifies Darwin’s procedure.

16 thoughts on “Stylized facts in ecology”

Nice post, but I don’t think you have to look to economists for inspiration. 🙂

A few quotes from ecologists:
“Macroecology is self-consciously expansive and synthetic … One way to do this is to stand back and take a sufficiently “distant view” that the idosyncratic details disappear and only the big, important features remain.”
” Brown’s 1995 book

“Macroecology … seeks to get above the mind-boggling details of local community assembly to find a bigger picture, whereby a kind of statistical order emerges from the scrum” John Lawton 1999

“To do science is to search for repeated patterns, not simply to accumulate facts” – MacArthur 1972

While people (correctly) focus on the large scale aspect of macroecology there is a clear methodological claim in the founding of macroecology too that seems to me extremely similar to “stylized facts” (and which I think even supposed macroecologists are starting to ignore at their peril).

I don’t think the nature of the stylized facts are different in macroecology. I just think the subject matters (or if you prefer variables of interest) are what differ. Scale of course often is different too but I really think that is the least important distinction. Its a question of variables. Do you care about total community abundance N, or periodicity of a single species population cycle. That is the only real difference I can see. The nature of the facts I would argue are highly similar.

“Do you care about total community abundance N, or periodicity of a single species population cycle. That is the only real difference I can see. ”

That’s not a big difference in the nature of the facts in your eyes? On the one hand are stylized facts that exist because they’re statistical attractors (or multiple realizability, or whatever your preferred term is). On the other hand are stylized facts that exist for, well, some other reason. Those different sorts of stylized facts are going to point towards different sorts of theoretical explanations, right? I mean, if you try to explain the universally lognormalish shape of species abundance distributions by appeal to, say, some quite specific model of predator-prey dynamics that you think applies to all communities, there are going to be tears before bedtime.

But in contrast, the right explanation for the Murdoch et al. 2002 stylized fact about predator-prey cycles lies in properties of specific predator-prey models (well, a class of predator-prey models). The explanation for the Bjornstad 2000 stylized fact lies in properties of a specific sort of coupled oscillator model. Etc. It’s the opposite of multiple realizability. There’s one specific model or class of models that captures the essence of the mechanism giving rise to the stylized fact. And stylized facts with different sorts of explanations seem to me to be different sorts of facts.

Not saying that one sort of stylized fact about one sort of variable (total abundance N or whatever) is intrinsically more interesting or important than a different sort of variable (single species population cycles or whatever). Just highlighting what seems to me to be an important difference between them.

Indeed, one doesn’t have to leave macroecology to find examples of stylized facts that don’t arise from multiple realizability. If West, Brown & Enquist are right, 3/4 power scaling of metabolic rate vs. body size arises because of evolutionary optimization of space-filling branching circulculatory systems. A very specific mechanistic model that applies to many species and so explains a comparative stylized fact about all those species. From where I sit, 3/4 power allometric scaling of metabolic rate with body size is the same sort of stylized fact as the ones from Murdoch et al. 2002 and Bjornstad 2000.

And I do think there’ve been times when ecologists have run into trouble by mismatching their stylized facts and the models with which they try to explain them. For instance, trying to explain the universally lognormalish shape of the species-abundance distribution by claiming that the dynamics of all communities are well-approximated by a model based on one specific mechanism (neutrality + drift).

I think there are plenty of “stylized/macroecological” facts that aren’t multiple attractor explained. yes lognormal distributions of abundance, range size and body size probably are. But the latitudinal gradient in richness? Or the elevational gradient in richness? Or Rapaports rule (range sizes covarying with latitude) or Bergman’s rule (body size covaryign with latitude). Or as macroecology gets more careful the covariation of richness with productivity, seasonaility and topographic heterogeneity. While none of these trace to predator prey models, I’m not sure why they’re innately different than Murdoch’s stylized fact about predator-prey cycles (macroecology sometimes even invokes claims about specialization vs generalization as did Murdoch (e.g. to explain why range size and local abundance and occupancy are correlated). And you already noted the 3/4 metabolic scaling which has physiological explanations.

Not trying to be difficult. Just not seeing once you cross off the lognormal pieces what the difference is?

@Brian:
p.s. to previous: I think our little now-resolved misunderstanding suggests highlights something interesting about those “foundational quotes of macroecology” you shared in an earlier comment. Those quotes are productively vague. Saying that one should zoom out/scale up/ignore idiosyncratic system-specific details/etc. can be interpreted to mean “look for statistical attractors/multiple realizability”. But it can *also* be interpreted to mean “look for a single universal mechanism, the effects of which are strong enough to shine through against the background noise of idiosyncratic system-specific details”. This is a quite productive bit of ambiguity if you’re looking to found an entire new subfield and get others to pursue it, because it considerably broadens the range of the subfield. Albeit perhaps at the long-term cost of making the subfield a bit inchoate? I seem to recall an old post in which you remarked that distinctions between macroecology and biogeography were blurring and that this was something of a mixed bag. Do you think the breakdown of that barrier, and the fact that it’s a mixed bag, trace back to that “creative ambiguity” in the foundational idea of macroecology?

Very interesting….but I remain sceptical on this: how can stylised facts be “not validly and rigorously inferred from reliable data”, yet still considered true as “empirical broad facts” ?
In my opinion, this infers a contradiction. Empirical broad facts aren’t by definition inferred from rigorous reliable data?

It’s a matter of how certain we are that something really is the case, and how certain we are of the domain over which it is the case. Is it really the case that synchrony of cycling populations generally breaks down when cycling is lost? I dunno–we only have a couple of suggestive examples to go on. To take a non-ecological example, several of Kaldor’s original stylized facts were based on data only from the US and UK, and have been revealed by subsequent research to be facts only about developed countries.

@Jeremy
Re creative ambiguity. I think you have put your finger on something important. It was definitely a case of creative ambiguity. And I think there was not necessarily agreement among the founders. I think Brian Maurer was very explicit in thinking of physics and statistical mechanics (which is more than just central limit theorem but still in that ball park of purely statistical explanations). And of course MaxEnt continues in that tradition. I don’t think Jim Brown saw it that way. And John Lawton was coming from the experience of feeling like his decades-long career on the community ecology of bracken fern herbivores was hopelessly contingent and was more moving away from something than towards a really specific vision. So yes I think that there was a creative ambiguity laid in the seeds of macroecology in part because of diverse views and in part because these were some really fertile minds who probably intuitively favored creative ambiguity.

That said, per the post you referenced, I think because of its ambiguity it has gradually been lost in people’s minds and most now equate macroecology solely as “anything with large scales” regardless of methodological or inferential approach. Hard to say whether that is bad or good. But I think it feels a bit odd to some of the macroecology old timers (like me, and, based on her comments on other posts here, perhaps Morgan Ernest too) who were attracted to macroecology more for the methodological reason than the scale reason. It is definitely something the field is working through at the moment.

Ok, it’s a somewhat different case, historically. Ecology wasn’t founded by a very small number of people who were self-consciously trying to define a new field or subfield, as with macroecology. But still, I think it’s an analogous case. Including the part about how creative ambiguity in the founding of the field sets the field up for arguments down the road about what it “really” is or ought to be.

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